Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences


Physics and Astronomy

First Advisor

Dr. Ganpathy Murthy

Second Advisor

Dr. Ribhu Kaul


Moiré materials, such as twisted bilayer graphene, have provided a rich platform for fundamental physics and potential technological applications. Superconductivity,
correlated insulators, and Chern insulators are examples of phenomena that have been found experimentally in moiré systems. The interplay of strong electron-electron interactions and topology lies at the heart of the mechanism driving these phenomena. In this work, we study the topological aspects of moiré graphene materials, such as the valley Chern and Chern insulating phases. To study the topological response of these phases, we construct models to describe the edge states which are the telltale signs of nontrivial topology. In the valley Chern insulator phase, we find absence of edge states at charge neutrality. This is attributed to the inter-valley scattering at the edges and suggests the importance of electron-electron interactions to understand the edge states of the valley Chern insulator realized in experiments. We provide an effective Hamiltonian to capture the quantum anomalous Hall state. Our model allows us to study the protected edge and domain wall states in this phase.

Digital Object Identifier (DOI)